Simple, step-by-step explanation for a 9-year-old of why the decimal point moves when multiplying or dividing by 10, 100, 1000, with easy rules and examples.
Our number system is base 10. That means each place value to the left is 10 times bigger than the one to its right. For example: hundreds, tens, ones, . , tenths, hundredths. Moving one place left multiplies by 10; moving one place right divides by 10.
When you multiply by 10, every digit moves one place to the left so the decimal point looks like it moved one place to the right. If you multiply by 100, digits move two places left (decimal moves right two places), and so on.
Easy rule: Count the zeros in 10, 100, 1000... Move the decimal that many places to the right.
Examples:
3.4 × 10 → move decimal 1 place right → 34
0.56 × 100 → move decimal 2 places right → 56
12.3 × 1000 → move decimal 3 places right → 12300
Dividing does the opposite. Each time you divide by 10 you move the decimal one place to the left. Divide by 100 → move two places left, etc.
Easy rule: Count the zeros in 10, 100, 1000... Move the decimal that many places to the left.
Examples:
45 ÷ 10 → move decimal 1 place left → 4.5
0.7 ÷ 100 → move decimal 2 places left → 0.007 (add zeros in front if you need them)
Each place is 10 times bigger than the one to its right. Multiplying by 10 makes every digit worth 10 times more, so digits must shift one place left. Writing that as moving the decimal is just a quick way to show the shift.
1) 2.3 × 10 = 23
2) 0.45 × 10 = 4.5
3) 7 ÷ 10 = 0.7
4) 5 ÷ 100 = 0.05
You're just shifting where the decimal point sits because each step left/right is a factor of 10. With practice it becomes quick and easy!